The ability to perceive the emotional state of others, empathy, is a natural mechanism evolved in the thinking of humans
[5].
Research has demonstrated that empathy has both a relationship with prosocial behaviors (actions taken for the benefit of others),
as well as a negative correlation with aggression
[2].
So imagine then, if every one of us became just a little bit more empathetic than we are right now; what impact might this have on a larger scale?
Moreover,
if an individual does desire to become more naturally empathetic,
how do they actually go about changing their ingrained thinking,
to achieve this?
This page shares one approach for attempting this: a very simple thought exercise which takes no more than a few minutes each day, which aims not to refine a person's ability to empathize,
but to generalize the scope of scenarios which cause them to empathize, by challenging them to continually identify situations in which they have no reason or inclination to empathize in and then, periodically and randomly, to empathize in those situations, even if it feels unnecessary or absurd to do so. Anecdotally, this exercise caused a profound (and lasting) change in how I empathize, and as a result, how I treat others. While I have no way to know if performing this exercise could have a similar impact on anyone else, I like to share it in case it might.

Empathy is the ability to understand what another being is experiencing, from within their frame of reference.
One form of empathy
is the emotional response that arises from witnessing another's emotions,
in such a way that our own emotions mirror what we are witnessing.
Suddenly, and without effort, it is as though we feel the other person's pain, or their joy, etc.
Empathy of this type is known as affective empathy, or emotional empathy
[4].
Here are some examples of affective empathy:

Feeling sadness, when we see someone cry over the death of a loved one.

Wincing when we witness someone being physically injured.

Humans can make the conscious decision to empathize, too.
This other type of empathy is often referred to as cognitive empathy, or colloquially as "picturing yourself in someone else's shoes"
[1].
Cognitive empathy involves two components:

You can go ahead and skip directly to the exercise if you'd like, which is highlighted below. However, I think it will be more effective, to first devote
a bit of thought to the following two points:

What situations cause you to (affectively) empathize?
We do not empathize in every situation; so which do cause us to empathize, and why?
Some believe that people will empathize towards situations which are relatable to them, while others think it stems from feelings of concern or engrained moral principles
[3].
How do you experience empathy in your life?
Which situations cause you to feel another person's pain/joy/etc.?
If you are a parent, you might empathize strongly when you see a young child crying.
If you are fond of animals, it might be seeing an animal in distress.
If you have experienced a particularly traumatic event, it might be witnessing someone deal with a similar trauma. These are just ideas; ponder what situations cause you to empathize easily.

Think about the various interactions/encounters you have with other individuals throughout your day.
It's easy to focus on direct, verbal communication - having a conversation with someone.
However, stop and consider all the ways you encounter others, even situations in which no direct communication occurs.
In essence, think of all the various
situations where another individual becomes part of your existence
for a moment in time.
This could be anything from an intimate conversation with a loved one, to
paying a cashier at the grocery store, sitting in a meeting, or making eye contact with a stranger when you're out for a walk.
Consider one sided situations as well: reading an email from your boss, watching the news, reading someone's opinion post on social media.
Think of unpleasant and frustrating interactions - is there someone you argue with frequently?
Maybe time spent on the phone disputing a medical bill,
getting pulled over by the police, or a dog that wakes you up early morning with its barking. Chances are, (for most people),
there are a myriad of ways they experience interconnectedness every day.

The Empathy Exercise: Do the following for one month: When you encounter others, ask yourself this question:
Is this a situation that would normally cause me to empathize? or, alternatively: Am I, (at this moment), empathizing with the individual(s) I am encountering/interacting with?
About once an hour, at random points throughout the day, when the answer to that question is 'no', devote a few moments
- 10 or 15 seconds - to cognitively empathizing with the individual(s) you are encountering.

An example:
Here is an example from my own experience with this exercise.
These are a few situations I began identifying, that I was not having a natural inclination to empathize in,
and so began empathizing in randomly:
driving to work (towards others drivers); reading generic business emails from executives in my company (towards those executives);
heated ethical debates (towards those I was debating/disagreeing with);
routine, emotionally neutral interactions with strangers such as buying groceries.
As for what I did in those moments,
I'd take a few seconds and imagine what that other person was experiencing.
(Were they frustrated, stuck in traffic? Bored at their job?
Angry/confused that I was disagreeing with viewpoints obvious to them?)
I'd imagine moments of joy in their lives, and moments of sadness.
I'd imagine mundane aspects of their lives (making breakfast, doing taxes...)
Since there was no reason to empathize in these moments, doing so did feel odd and unnatural at first.
But (very quickly) it led to some dramatic shifts in how I viewed those around me, and as a result, how I treated them.
Furthermore, because the situations/targets of empathizing were random, the perspective
shift was a general one, rather than being limited to specific individuals or groups.
Rather than bias you by explaining the changes I experienced, discover what (if any) impact it has for you (if you'd like to try it out that is). Best wishes!
References: